On the SY-80 board, take a look at capacitors C28 (22uF/25v) and C29 (1uF / 50v). They're both part of the CPU reset logic, and the purpose is to give the power supply time to come up completely and the rest of the machine to be fully powered before releasing the reset inputs to the CPUs on SY-80, SY-79, and LG-02 boards. If one of these caps is leaky (electrically), the time delay will increase -- or it might never allow the reset line to rise.